Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-02-01T02:12:13.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinetic energy transfer in compressible isotropic turbulence

Published online by Cambridge University Press:  26 February 2018

Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window] ,
Minping Wan ,
Song Chen  and
Shiyi Chen
Jianchun Wang*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Minping Wan*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Song Chen
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Shiyi Chen
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China State Key Laboratory of Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Kinetic energy transfer in compressible isotropic turbulence is studied using numerical simulations with solenoidal forcing at turbulent Mach numbers ranging from 0.4 to 1.0 and at a Taylor Reynolds number of approximately 250. The pressure dilatation plays an important role in the local conversion between kinetic energy and internal energy, but its net contribution to the average kinetic energy transfer is negligibly small, due to the cancellation between compression and expansion work. The right tail of probability density function (PDF) of the subgrid-scale (SGS) flux of kinetic energy is found to be longer at higher turbulent Mach numbers. With an increase of the turbulent Mach number, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux. Average of SGS flux conditioned on the filtered velocity divergence is studied by numerical analysis and a heuristic model. The conditional average of SGS flux is shown to be proportional to the square of filtered velocity divergence in strong compression regions for turbulent Mach numbers from 0.6 to 1.0. Moreover, the antiparallel alignment between the large-scale strain and the SGS stress is observed in strong compression regions. The inter-scale transfer of solenoidal and compressible components of kinetic energy is investigated by Helmholtz decomposition. The SGS flux of solenoidal kinetic energy is insensitive to the change of turbulent Mach number, while the SGS flux of compressible kinetic energy increases drastically as the turbulent Mach number becomes larger. The compressible mode persistently absorbs energy from the solenoidal mode through nonlinear advection. The kinetic energy of the compressible mode is transferred from large scales to small scales through the compressible SGS flux, and is dissipated by viscosity at small scales.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 581 - 613
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aluie, H. & Eyink, G. L. 2009 Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter. Phys. Fluids 21, 115108.CrossRefGoogle Scholar
Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.CrossRefGoogle ScholarPubMed
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29.CrossRefGoogle Scholar
Aluie, H. 2013 Scale decomposition in compressible turbulence. Physica D 247, 54–65.Google Scholar
Anderson, B. W. & Domaradzki, J. A. 2012 A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence. Phys. Fluids 24, 065104.CrossRefGoogle Scholar
Balsara, D. S. & Shu, C. W. 2000 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160, 405–452.CrossRefGoogle Scholar
Benzi, R., Biferale, L., Fisher, R. T., Kadanoff, L. P., Lamb, D. Q. & Toschi, F. 2008 Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev. Lett. 100, 234503.CrossRefGoogle ScholarPubMed
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Cerutti, S. & Meneveau, C. 1997 Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence. Phys. Fluids 10, 928–937.CrossRefGoogle Scholar
Cimarelli, A. & Angelis, E. D. 2014 The physics of energy transfer toward improved subgrid-scale models. Phys. Fluids 26, 055103.CrossRefGoogle Scholar
Domaradzki, J. A., Liu, W. & Brachet, M. E. 1993 An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5, 1747–1759.CrossRefGoogle Scholar
Domaradzki, J. A. & Carati, D. 2007a A comparison of spectral sharp and smooth filters in the analysis of nonlinear interactions and energy transfer in turbulence. Phys. Fluids 19, 085111.Google Scholar
Domaradzki, J. A. & Carati, D. 2007b An analysis of the energy transfer and the locality of nonlinear interactions in turbulence. Phys. Fluids 19, 085112.Google Scholar
Domaradzki, J. A. & Saiki, E. M. 1997 Backscatter models for large-Eddy simulations. Theor. Comput. Fluid Dyn. 9, 75–83.CrossRefGoogle Scholar
Domaradzki, J. A., Teaca, B. & Carati, D. 2009 Locality properties of the energy flux in turbulence. Phys. Fluids 21, 025106.CrossRefGoogle Scholar
Eyink, G. L. 2005 Locality of turbulent cascades. Physica D 207, 91–116.Google Scholar
Eyink, G. L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys. Fluids 21, 115107.CrossRefGoogle Scholar
Falkovich, G., Fouxon, I. & Oz, Y. 2010 New relations for correlation functions in Navier–Stokes turbulence. J. Fluid Mech. 644, 465–472.CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2007 Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335–366.CrossRefGoogle Scholar
Jagannathan, S. & Donzis, D. A. 2016 Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations. J. Fluid Mech. 789, 669–707.CrossRefGoogle Scholar
Jimenez, J. & Moser, R. D. 2000 Large-eddy simulations: where are we and what can we expect? AIAA J. 38, 605–612.CrossRefGoogle Scholar
Kerr, R. M., Domaradzki, J. A. & Barbier, G. 1995 Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids 8, 197–208.CrossRefGoogle Scholar
Kida, S. & Orszag, S. A. 1992 Energy and spectral dynamics in decaying compressible turbulence. J. Sci. Comput. 7, 1–34.CrossRefGoogle Scholar
Kritsuk, A. G., Wagner, R. & Norman, M. L. 2013 Energy cascade and scaling in supersonic isothermal turbulence. J. Fluid Mech. 729, R1.CrossRefGoogle Scholar
Lee, S., Lele, S. K. & Moin, P. 1991 Eddy shocklets in decaying compressible turbulence. Phys. Fluids A 3, 657–664.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Livescu, D. & Li, Z. 2017 Subgrid-scale backscatter after the shock-turbulence interaction. AIP Conf. Proc. 1793, 150009.CrossRefGoogle Scholar
Livescu, D. & Ryu, J. 2016 Vorticity dynamics after the shock-turbulence interaction. Shock Waves 26, 241–251.CrossRefGoogle Scholar
Martin, M. P., Piomelli, U. & Candler, G. V. 2000 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13, 361–376.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Miura, H. & Kida, S. 1995 Acoustic energy exchange in compressible turbulence. Phys. Fluids 7, 1732–1742.CrossRefGoogle Scholar
O’Brien, J., Urzay, J., Ihme, M., Moin, P. & Saghafian, A. 2014 Subgrid-scale backscatter in reacting and inert supersonic hydrogenCair turbulent mixing layers. J. Fluid Mech. 743, 554–584.CrossRefGoogle Scholar
O’Brien, J., Towery, C. A. Z., Hamlington, P. E., Ihme, M., Poludnenko, A. Y. & Urzay, J. 2017 The cross-scale physical-space transfer of kinetic energy in turbulent premixed flames. Proc. Combust. Inst. 36, 1967–1975.CrossRefGoogle Scholar
Petersen, M. R. & Livescu, D. 2010 Forcing for statistically stationary compressible isotropic turbulence. Phys. Fluids 22, 116101.CrossRefGoogle Scholar
Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 1766–1771.CrossRefGoogle Scholar
Pirozzoli, S. & Grasso, F. 2004 Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16, 4386–4407.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Quadros, R., Sinha, K. & Larsson, J. 2016 Turbulent energy flux generated by shock/homogeneous-turbulence interaction. J. Fluid Mech. 796, 113–157.CrossRefGoogle Scholar
Ryu, J. & Livescu, D. 2014 Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756, R1.CrossRefGoogle Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompresible Flows, 3rd edn. Springer Science & Business Media.Google Scholar
Samtaney, R., Pullin, D. I. & Kosovic, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13, 1415–1430.CrossRefGoogle Scholar
Suman, S. & Girimaji, S. S. 2011 Dynamical model for velocity-gradient evolution in compressible turbulence. J. Fluid Mech. 683, 289–319.CrossRefGoogle Scholar
Tao, B., Katz, J. & Meneveau, C. 2002 Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech. 457, 35–78.CrossRefGoogle Scholar
Tian, Y., Jaberi, F. A., Li, Z. & Livescu, D. 2017 Numerical study of variable density turbulence interaction with a normal shock wave. J. Fluid Mech. 829, 551–588.CrossRefGoogle Scholar
Towery, C. A. Z., Poludnenko, A. Y., Urzay, J., O’Brien, J., Ihme, M. & Hamlington, P. E. 2016 Spectral kinetic energy transfer in turbulent premixed reacting flows. Phys. Rev. E 93, 053115.Google ScholarPubMed
Wagner, R., Falkovich, G., Kritsuk, A. G. & Norman, M. L. 2012 Flux correlations in supersonic isothermal turbulence. J. Fluid Mech. 713, 482–490.CrossRefGoogle Scholar
Wan, M., Oughton, S., Servidio, S. & Matthaeus, W. H. 2010 On the accuracy of simulations of turbulence. Phys. Plasmas 17, 082308.CrossRefGoogle Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017a Spectra and statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2, 013403.Google Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017b Shocklet statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2, 023401.Google Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017c Scaling and intermittency in compressible isotropic turbulence. Phys. Rev. Fluids 2, 053401.Google Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. T. & Chen, S. 2011 Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence. Phys. Fluids 23, 125103.CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. T. & Chen, S. 2012a Effect of compressibility on the small scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631.CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. T. & Chen, S. 2012b Scaling and statistics in three-dimensional compressible turbulence. Phys. Rev. Lett. 108, 214505.CrossRefGoogle ScholarPubMed
Wang, J., Wang, L.-P., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229, 5257–5259.CrossRefGoogle Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2013 Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505.CrossRefGoogle ScholarPubMed
Yang, Y., Matthaeus, W. H., Parashar, T. N., Haggerty, C. C., Roytershteyn, V., Daughton, W., Wan, M., Shi, Y. & Chen, S. 2017a Energy transfer, pressure tensor, and heating of kinetic plasma. Phys. Plasmas 24, 072306.CrossRefGoogle Scholar
Yang, Y., Matthaeus, W. H., Parashar, T. N., Wu, P., Wan, M., Shi, Y., Chen, S., Roytershteyn, V. & Daughton, W. 2017b Energy transfer channels and turbulence cascade in Vlasov–Maxwell turbulence. Phys. Rev. E 95, 061201(R).Google ScholarPubMed
Yang, Y., Matthaeus, W. H., Shi, Y., Wan, M. & Chen, S. 2017c Compressibility effect on coherent structures, energy transfer, and scaling in magnetohydrodynamic turbulence. Phys. Fluids 29, 035105.CrossRefGoogle Scholar
Yang, Y., Shi, Y., Wan, M., Matthaeus, W. H. & Chen, S. 2016a Energy cascade and its locality in compressible magnetohydrodynamic turbulence. Phys. Rev. E 93, 061102.Google ScholarPubMed
Yang, Y., Wang, J., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2016b Intermittency caused by compressibility: a Lagrangian study. J. Fluid Mech. 786, R6.CrossRefGoogle Scholar